Double-sided aspheric varifocal power lens

ABSTRACT

To provide a bi-aspherical type progressive-power lens which provides an excellent visual acuity correction for prescription values and a wide effective visual field with less distortion in wearing, by reducing a magnification difference of an image between a distance portion and a near portion. The lens is characterized in that when on a first refractive surface being an object side surface, a surface refractive power in a horizontal direction and a surface refractive power in a vertical direction, at a far vision diopter measurement position F 1 , are DHf and DVf respectively, and on the first refractive surface, a surface refractive power in a horizontal direction and a surface refractive power in a vertical direction, at a near vision diopter measurement position N 1 , are DHn and DVn respectively, relational equations, 
       DHf+DHn&lt;Dvf+DVn , and  DHn&lt;DVn   
     are satisfied, and surface astigmatism components at F 1  and N 1  of the first refractive surface are cancelled by the second refractive surface being an eyeball side surface so that the first and second refractive surfaces together provide a far vision diopter (Df) and an addition diopter (ADD) based on prescription values.

TECHNICAL FIELD

[0001] The present invention relates to a bi-aspherical typeprogressive-power lens, which is a lens used as, for example, aprogressive-power lens for a spectacle for presbyopia that is configuredto have a progressive refractive power action dividedly allotted to afirst refractive surface being an object side surface and a secondrefractive surface being an eyeball side surface, so that the firstsurface and the second surface together provide a far vision diopter(Df) and an addition diopter (ADD) based on prescription values.

BACKGROUND ART

[0002] A progressive-power lens is widely used in general because of anadvantage that it is hardly detected from others as a spectacle for theaged in spite of a spectacle lens for presbyopia, an advantage that itallows a wearer to clearly look continuously from a far distance to anear distance without discontinuity, and so on. However, it is alsowidely known that the necessity of arrangement of a plurality of visualfields such as a field for looking far and a field for looking near, andfurther a field for looking at a distance intermediate therebetween,without a boundary line existing within a limited lens area, presentsdisadvantages specific to the progressive-power lens such that eachvisual field is not always sufficiently wide, and that there is a regionmainly in a side visual field which causes the wearer to feel distortionor sway of an image.

[0003] Various proposals have been made since long ago to improve thedisadvantages specific to the progressive-power lens, and most of suchconventional progressive-power lenses have a surface configurationcreated by a combination of a “progressive surface” arranged on anobject side surface and a “spherical surface” or a “cylindrical surface”arranged on an eyeball side surface. Conversely to those,Atoral-Variplas as a progressive-power lens, which is characterized inthat a “progressive action” is added to the eyeball side surface, isreleased in 1970 from Essel Optical Co. (now Essilor), France.

[0004] Besides, recently proposed prior arts include, for example,technologies described in Patent International Publication Nos. WO97/19382 and WO 97/19383 and so on, which are generally called rearsurface progression (or concave surface progression). The surfaceconfiguration in the recently proposed rear surface progression has amain purpose of improving distortion and sway of an image by allotting aportion or the whole of a necessary addition diopter from an object sidesurface to an eyeball side surface to reduce the magnificationdifference of an image between a distance portion and a near portion.

[0005] Among these prior arts, one described in WO 97/19382 has aconfiguration in which the object side surface is made a sphericalsurface or a rotationally symmetrical aspherical surface to completelycancel the “progressive action,” and a “progressive surface” providing apredetermined addition diopter is added (fused) to only the eyeball sidesurface. Besides, the prior art described in WO 97/19383 has aconfiguration in which the addition diopter on the “progressive surface”being the object side surface is made lower than a predetermined valueand a “progressive surface” providing a deficiency in addition diopteris added (fused) to a “spherical surface” or “cylindrical surface” onthe rear surface side.

[0006] Although having different purposes and reasons, other prior artsof the progressive-power lens having description of technologies ofadding the “progressive action” to the eyeball side surface, include,for example, ones described in Japanese Patent Publication No. Sho47-23943, Japanese Patent Laid-Open No. Sho 57-10112, Japanese PatentLaid-Open No. Hei 10-206805, and Japanese Patent Laid-Open No.2000-21846. In addition, prior arts in which the “progressive action” isprovided to both surfaces of a lens, as in one described in theaforementioned WO 97/19383, include ones described in Japanese PatentLaid-Open No. 2000-338452 and Japanese Patent Laid-Open No. Hei6-118353. Commonly, in these prior arts, front and rear two surfacestogether provide a necessary addition diopter.

[0007] These prior arts have a main purpose of improving distortion andsway of an image by allotting a portion or the whole of a necessaryaddition diopter on an object side surface to an eyeball side surface toreduce magnification difference between a distance portion and a nearportion. Clear description, however, on reasons of their improvedeffects can be rarely found, and only partial description thereof isfound just in the aforementioned Patent International Publication No. WO97/19383 (hereinafter, Prior art 1) or the like. Namely, Prior art 1discloses the following calculation equations for a lens magnificationSM shown in the equation (1) to the equation (3), the lens magnificationSM is used as a basic evaluation parameter for lens design.

[0008] Namely, Prior art 1 includes the following description.

[0009] “The lens magnification SM is generally expressed by thefollowing equation.

SM=Mp×Ms  (1),

[0010] where Mp is called a power factor, and Ms is called a shapefactor. When the distance from a vertex of an eyeball side surface(inside vertex) of a lens to an eyeball is an inter-vertex distance L, arefractive power at the inside vertex (inside vertex refractive power)is Po, a thickness at the center of the lens is t, a refractive index ofthe lens is n, and a base curve (refractive power) of the object sidesurface of the lens is Pb, Mp and Ms are expressed as follows.

Mp=1/(1−L×Po)  (2)

Ms=1/(1−(t×Pb)/n)  (3)

[0011] It should be noted that for calculations of the equation (2) andthe equation (3), dioptry (D) is used for the inside vertex refractivepower Po and the base curve Pb, and meter (m) is used for the distance Land thickness t, respectively.”

[0012] Then, these calculation equations for the lens magnification SMare used to calculate a difference in magnification between a distanceportion and a near portion. In Prior art 1, it is regarded that thedistortion and sway of an image are improved because of a smallmagnification difference.

[0013] The study by the inventor of the invention shows that though someeffects are recognized in the above-described Prior art 1 as compared toits prior art, the following points need to be discussed to design alens with higher performance.

[0014] a. Basic evaluation parameters used in the above-described Priorart 1 include a parameter which should be essentially applied only to aportion near the center of a lens as is clear from the description of“the distance L from a vertex of an eyeball side surface of a lens to aneyeball” and “a thickness t at the center of the lens.” Morespecifically, in an example of Prior art 1, the basic evaluationparameter to be applied only to a distance portion near the center ofthe lens, is applied also to a near portion positioned at a greatdistance below the lens center, thus presenting a possibility of error.

[0015] b. In Prior art 1, the lens magnification SM is calculated usingfive basic evaluation parameters, composed of the aforementioned oneswith addition of the “refractive index of the lens n.” However, as isinstantly found when tilting forward and backward a lens having anactual diopter, it is considered that the size of an image is stronglyinfluenced by an “angle between a sight line and a lens surface.” Thisleads to a consideration that the “angle between a sight line and a lenssurface” is nonnegligible particularly in calculation of themagnification of the near portion positioned at a great distance belowthe lens center. Accordingly, the lens design of Prior art 1 has apossibility of error caused by the “calculation of the lensmagnification without consideration of the angle between a sight lineand a lens surface.”

[0016] c. Prior art 1 only describes the “magnification” for anapplication example to a cylindrical lens but lacks idea on directionthereof, which causes a possibility of error when “magnifications in thevertical direction and the horizontal direction are different” whichoccurs, for example, in the near portion positioned at a great distancebelow the lens center.

[0017] d. To accurately calculate the magnification for the nearportion, the distance to a visual target, that is, an “object distance”should be added as a calculation factor. In Prior art 1, the “objectdistance” is not taken into consideration, which presents an undeniablepossibility of error.

[0018] e. In the magnification calculations, the influence by a prismaction is not taken into consideration, which may cause an error.

[0019] As described above, the prior art may not be always sufficientfrom a viewpoint, in particular, of more accurately calculating the“magnification.”

[0020] The present invention is made to solve the above problems, andits object is to provide a bi-aspherical type progressive-power lenswhich provides an excellent visual acuity correction for prescriptionvalues and a wide effective visual field with less distortion inwearing, by reducing a magnification difference of an image between adistance portion and a near portion through correct calculation of themagnification of the image with an influence by an “angle between asight line and a lens surface” and an “object distance” taken intoconsideration.

[0021] It is another object of the present invention to provide abi-aspherical type progressive-power lens which makes it possible to usea “bilaterally symmetrical semifinished product” as an object sidesurface and process after acceptance of an order only an eyeball sidesurface into a bilaterally asymmetrical curved surface coping with aconvergence action of an eye in near vision, and to reduce processingtime and cost.

DISCLOSURE OF THE INVENTION

[0022] As means to solve the above-described problems, in a first means,

[0023] in a bi-aspherical type progressive-power lens with a progressiverefractive power action dividedly allotted to a first refractive surfacebeing an object side surface and a second refractive surface being aneyeball side surface,

[0024] when on the first refractive surface, a surface refractive powerin a horizontal direction and a surface refractive power in a verticaldirection, at a far vision diopter measurement position F1, are DHf andDVf respectively, and

[0025] on the first refractive surface, a surface refractive power in ahorizontal direction and a surface refractive power in a verticaldirection, at a near vision diopter measurement position N1, are DHn andDVn respectively, relational equations,

DHf+DHn<Dvf+DVn, and DHn<DVn

[0026] are satisfied, and surface astigmatism components at F1 and N1 ofthe first refractive surface are cancelled by the second refractivesurface so that the first and second refractive surfaces togetherprovide a far vision diopter (Df) and an addition diopter (ADD) based onprescription values.

[0027] In a second means,

[0028] in the bi-aspherical type progressive-power lens according to thefirst means, relational equations DVn−DVf>ADD/2, and DHn−DHf<ADD/2 aresatisfied.

[0029] In a third means,

[0030] in the bi-aspherical type progressive-power lens according to thefirst or second means, the first refractive surface is bilaterallysymmetrical with respect to one meridian passing through the far visiondiopter measurement position F1, the second refractive surface isbilaterally symmetrical with respect to one meridian passing through afar vision diopter measurement position F2 of the second refractivesurface, and a position of a near vision diopter measurement position N2on the second refractive surface is shifted inward to a nose by apredetermined distance to respond to a convergence action of an eye innear vision.

[0031] In a fourth means,

[0032] in the bi-aspherical type progressive-power lens according to anyone of the first to the third means, the first refractive surface is arotation surface with as a generatrix one meridian passing through thefar vision diopter measurement position F1, the second refractivesurface is bilaterally symmetrical with respect to one meridian passingthrough a far vision diopter measurement position F2 on the secondrefractive surface, and a position of a near vision diopter measurementposition N2 on the second refractive surface is shifted inward to a noseby a predetermined distance to respond to a convergence action of an eyein near vision.

[0033] In a fifth means,

[0034] in the bi-aspherical type progressive-power lens according to anyone of the first to the fourth means, in a configuration of the firstand second refractive surfaces together providing the far vision diopter(Df) and the addition diopter (ADD) based on the prescription values,occurrence of astigmatism and change in diopter caused by impossibilityof a sight line intersecting with at right angles with a lens surface ina wearing state are reduced.

[0035] The above-described means are devised based on the followingresults of clarification. Hereinafter, description will be made withreference to the drawings. FIG. 1 is an explanatory view of varioussurface refractive powers at positions on a spectacle lens surface, FIG.2 is an explanatory view of a positional relation among an eyeball,sight lines, and a lens, FIG. 3-1, FIG. 3-2, and FIG. 3-3 and FIG. 4-1,FIG. 4-2, and FIG. 4-3 are explanatory views on a magnification Mγ of aprism, being explanatory views on a difference between a plus lens and aminus lens and on a difference in magnification in viewing mainly usinga near portion which is a lower portion of a lens, FIG. 5-1 is anexplanatory view of an optical layout of progressive-power lens, being afront view of the progressive power lens when viewed from an object sidesurface, FIG. 5-2 is an explanatory view of the optical layout of theprogressive-power lens, being a side view illustrating a cross sectionin the vertical direction, FIG. 5-3 is an explanatory view of theoptical layout of the progressive-power lens, being an elevational viewillustrating a cross section in the transverse direction, and FIG. 6 isan explanatory view illustrating the difference of definition on“addition diopter.” Note that in these drawings, symbol F denotes a farvision diopter measurement position, symbol N denotes a near visiondiopter measurement position, and symbol Q denotes a prism dioptermeasurement position. In addition, other symbols shown in FIG. 1 and soon denote,

[0036] DVf: surface refractive power at F of a sectional curved line inthe vertical direction passing through F,

[0037] DVn: surface refractive power at N of a sectional curved line inthe vertical direction passing through N,

[0038] DHf: surface refractive power at F of a sectional curved line inthe horizontal direction passing through F, and

[0039] DHn: surface refractive power at N of a sectional curved line inthe horizontal direction passing through N. Further, suffix 1 is addedto all of the symbols when the refractive surface of a drawing is afirst refractive surface being the object side surface, and suffix 2 isadded to all of the symbols when the surface is a second refractivesurface being the eyeball side surface for recognition.

[0040] Besides, symbols F1 and F2 denote far vision diopter measurementpositions on the object side surface and the eyeball side surface, andsimilarly symbols N1 and N2 denote near vision diopter measurementpositions on the object side surface and the eyeball side surface.Further, symbol E is an eyeball, symbol C a center of rotation of theeyeball, symbol S a reference surface around C, symbols Lf and Ln sightlines passing through the far vision diopter measurement position andnear vision diopter measurement position respectively. Besides, symbol Mis a curved line called a main gazing line through which a sight linepasses when one looks with both eyes from an upper front to a lowerfront portion. Then, symbols F1, N1, F2, N2, and N3 indicate positions,to which an opening of a lens meter is placed, differing depending onthe definition of the “addition diopter.”

[0041] First, a calculation equation of a magnification corresponding tothe near vision improved by “corresponding parameters to the nearportion” which is the problem (a) of the above-described prior art and“considering the object distance” which is the problem (d), was designedto be obtained as follows. Namely, when Mp is a power factor and Ms is ashape factor, a magnification SM of an image is expressed by

SM=Mp×Ms  (1′).

[0042] Here, when the objective power (inverse number of the objectdistance expressed in a unit of m) to a visual target is Px, thedistance from the eyeball side surface in the near portion of the lensto the eyeball is L, the refractive power in the near portion (insidevertex refractive power in the near portion) is Po, the thickness in thenear portion of the lens is t, the refractive index of the lens is n,and the base curve (refractive power) of the object side surface in thenear portion of the lens is Pb, the following relation is established.

Mp=(1−(L+t)Px)/(1−L×Po)  (2′)

Ms=1/(1−t×(Px+Pb)/n)  (3′)

[0043] These equations, in which the parameters are made to correspondto the distance portion, and 0 corresponding to infinity is substitutedfor Px indicating power of the object distance, match the equations ofthe above-described Prior art 1. In other words, the equations used inPrior art 1 can be considered to be equations dedicated for the farvision having an infinitive object distance. By the way, although theequation (1′) here is identical to the equation of the above-describedPrior art 1, the object distance in near vision is generally about 0.3 mto about 0.4 m, and thus Px which is the inverse number thereof becomesa value from about −2.5 to about −3.0. Accordingly, Mp increases in theequation (2′) because the numerator increases, and Ms decreases in theequation (3′) because the denominator increases. This shows that theinfluence by the shape factor Ms in the near vision is less than that bythe calculations of Prior art 1. For example, when Pb=−Px, that is, thebase curve (refractive power) of the surface on the object side of alens has a value ranging from about +2.5 to about +3.0, Ms=1, whichshows that the shape factor in the near vision is completely irrelevantto the magnification of an image.

[0044] Although, in the above-described manner, the calculationequations for magnification with the parameters corresponding to thenear portion and the “object distance” taken into consideration havebeen obtained, the “angle between a sight line and a lens surface” whichis the problem (b) of the above-described Prior art 1 also needs to betaken into consideration to calculate a magnification in actual nearvision. What is an important here is that the “angle between a sightline and a lens surface” has a directional property. In other words,taking the “angle between a sight line and a lens surface” intoconsideration is nothing but concurrently taking into consideration thedirectional property of the “magnification of an image” which is theproblem (c) of the above-described Prior art 1.

[0045] Reviewing the first calculation equation of the above-describedequations (1′) to (3′) in this viewpoint, it has as calculation factorsinfluenced by the “angle between a sight line and a lens surface,” theinside vertex refractive power Po in the near portion and the base curve(refractive power) Pb of the object side surface in the near portion.Here, when well-known Martin's approximate equations are used, with theangle formed between the sight line in near vision and the optical axisof the region in the near portion being α and the angle formed betweenthe sight line in the near vision and the normal line on the object sidesurface in the near portion being β,

[0046] the inside vertex refractive power in the vertical direction inthe near portion:

Pov=Po×(1+Sin 2α×4/3),

[0047] the inside vertex refractive power in the horizontal direction inthe near portion:

Poh=Po×(1+Sin 2α×1/3),

[0048] the vertical section refractive power on the object side surfacein the near portion:

Pbv=Pb×(1+Sin 2β×4/3), and

[0049] the transverse section refractive power on the object sidesurface in the near portion:

Pbh=Pb×(1+Sin 2β×1/3).

[0050] As long as the angles α and β and Po and Pb are not zero, therefractive powers, power factors, and shape factors have differentvalues between the vertical and horizontal directions as describedabove, resulting in a difference in magnification occurring between thevertical direction and the horizontal direction.

[0051] By the way, while the approximate equations are used here toexplain simply a fact that “the refractive power varies depending on thedirection of the sight line,” these values are desirably obtained byaccurate ray tracing calculation in the actual optical design. In anonattributive example of the method of calculating these, for example,an optical path along the sight line is calculated using Snell's law tocalculate L, t, and the distance from the object side refractive surfaceto an object point, and then, along-this optical path, the firstfundamental form, the second fundamental form, Weingarten formula, orthe like in differential geometry can be used to calculate therefractive power with the influence of refraction on the optical path onthe object side refractive surface and the eyeball side refractivesurface taken into consideration. These equations and formula andcalculating methods are known from long ago and described in a knownliterature “Differential Geometry” (written by Kentaro Yano, publishedby Asakura Shoten Kabusikikaisya, the first edition, 1949) and so on,and thus the description thereof is omitted.

[0052] By the way, by performing such accurate ray tracing calculations,four calculation factors L, Po, t, and Pb which are the above-describedproblems (a) to (d) are taken into consideration, and accuratemagnification calculations can be possible in all of sight linedirections as well as in the near portion located at a great distancebelow the lens center. In such a manner, the above-described items,

[0053] the inside vertex refractive power in the vertical direction inthe near portion: Pov,

[0054] the inside vertex refractive power in the horizontal direction inthe near portion: Poh,

[0055] the vertical section refractive power on the object side surfacein the near portion: Pbv, and the transverse section refractive power onthe object side surface in the near portion: Pbh, can be obtained at anaccuracy higher than that in a case using Martin's approximateequations.

[0056] It will be easily understood that all of the above-describedmagnification calculations of an image have to correspond to thedifference in the direction of the sight line from the fact that the“the refractive power varies in accordance with the direction of thesight line,” as described above. Here, when Mp is the power factor andMs is the shape factor, and suffix v is added for the vertical directionand suffix h is added for the horizontal direction to express themagnification SM of an image, the above-described equations (1′) to (3′)are rewritten as follows:

SMv=Mpv×Msv  (1v′)

SMh=Mph×Msh  (1h′)

Mpv=(1−(L+t)Px)/(1−L×Pov)  (2v′)

Mph=(1−(L+t)Px)/(1−L×Poh)  (2h)

Msv=1/(1−t×(Px+Pbv)/n)  (3v′)

Msh=1/(1−t×(Px+Pbh)/n)  (3h′).

[0057] The above way could cope with the above-described problems (a) to(d) of Prior art 1. At last, the “influence by the prism action” whichis the above-described problem (e) in calculating the magnification inthe actual near vision will be described. While a prism itself has norefractive power unlike a lens, the magnification Mγ of the prism variesdepending on the incident angle and exit angle of rays to/from theprism. Here, an angle magnification γ when a ray incident from a vacuumto a medium with a refractive index n, as shown on the left side in FIG.3-1 and FIG. 4-1, is refracted on the surface of the medium isconsidered. When the incident angle is i and the refractive angle is γin this event, n=Sin i/Sin r by well-known Snell's law. Besides, theangle magnification γ by refraction is expressed by γ=Cos i/Cos r. Sincen≧1, generally i≧r and γ≦1. Here, γ becomes a maximum value 1 wheni=r=0, that is, in the case of a normal incidence. When the refractiveangle r is as n=1/Sin r, γ becomes a theoretical minimum value, γ=0. Atthis time, i=π/2, and thus r is equal to a critical angle of totalreflection when a ray exits from the medium.

[0058] On the other hand, an angle magnification γ′ when a ray exitsfrom a medium with a refractive index of n to a vacuum, as shown on theright side in FIG. 3-1 and FIG. 4-1, becomes completely reverse to theabove. More specifically, when the incident angle of a ray, which isrefracted on a medium surface and exits from within the medium to avacuum, is i′ and the refractive angle is r′, 1/n=Sin i′/Sin r′ bySnell's law, and the angle magnification is expressed by γ′=Cos i′/Cosr′. Since n≧1, generally r′≧i′ and γ′≧1. Here, γ′ becomes a maximumvalue 1 when i′=r′=0, that is, in the case of a normal incidence. Whenthe incident angle i′ is as n=1/Sin i′, γ′ becomes a theoretical maximumvalue, γ′=∞. At this time, r′=π/2, and thus i′ is equal to a criticalangle of total reflection when a ray exits from the medium.

[0059] As shown in FIG. 3-3 and FIG. 4-3, a case in which a ray incidenton the object side surface of one spectacle lens passes through theinside of the lens, exits from the eyeball side surface, and reaches aneyeball, is considered (hereinafter, it should be convenientlyconsidered that the refractive index of air is approximated to be 1 thatis the same as in a vacuum to simplify description). When the refractiveindex of a spectacle lens is n, the incident angle of a ray incident onthe object side surface is i, the refractive angle is r, the incidentangle of a ray from within the lens reaching the eyeball side surface isi′, and the refractive angle of an emergent ray is r′, the anglemagnification Mγ passing through the two surfaces of the spectacle lensis expressed by a product of the above-described two kinds of anglemagnifications,

Mγ=γ×γ′=(Cos i×Cos i′)/(Cos r×Cos r′).

[0060] This is irrelevant to the refractive power on the lens surfaceand known as a magnification of a prism.

[0061] Here, when a case of i=r′ and r=i′ as shown in FIG. 3-1 and FIG.4-1 is considered,

Mγ=γ×γ′=1,

[0062] which means that there is no change in magnification of an imageseen through a prism. Meanwhile, when a ray is perpendicularly incidenton the object side surface of the spectacle lens as shown in FIG. 3-2,

Mγ=γ′=Cos i′/Cos r′≧1,

[0063] and conversely, when a ray perpendicularly exits from the eyeballside surface of the spectacle lens as shown in FIG. 4-2,

Mγ=γ=Cos i/Cos r≦1.

[0064] Here, what is important is that the magnifications Mγ of a prismhave a directional property. More specifically, when the distribution ofprisms in a progressive-power lens is considered, it naturally variesdepending on the diopter and prescription prism value, in whichgenerally prisms in the far vision near the lens center are small andprisms in the vertical direction in the near vision located at a lowerportion of the lens are large. Therefore, it can be said that themagnification Mγ of the prism has great influence especially on thevertical direction in the near vision.

[0065] Not only a progressive-power lens, but also a typical spectaclelens has a meniscus shape in which the object side surface is convex andthe eyeball side surface is concave, and thus taking it intoconsideration that the sight line in near vision is in a downwarddirection, it can be said that the near vision through theprogressive-power lens having a positive refractive power in the nearportion as shown in FIG. 3-3, is similar to the shape in FIG. 3-2 ofMγ≧1 rather than in FIG. 3-1 of Mγ=1, and at least Mγ≧1. Similarly, itcan be said that the near vision through the progressive-power lenshaving a negative refractive power in the near portion as shown in FIG.4-3, is similar to the shape in FIG. 4-2 of Mγ≦1 rather than in FIG. 4-1of Mγ=1, and at least Mγ<1. Accordingly, Mγ >1 in the near visionthrough the progressive-power lens having a positive refractive power inthe near portion, and Mγ<1 in the near vision through theprogressive-power lens having a negative refractive power in the nearportion.

[0066] While the magnification SM of the lens in Prior art 1 is graspedonly as a product of the power factor Mp and the shape factor Ms asdescribed above, the present invention aims to further multiply theproduct by the magnification Mγ of a prism to obtain a correctmagnification of a lens.

[0067] The magnification Mγ by a prism is called a “prism factor” incontrast with Mp and Ms, and when suffix v is added for the verticaldirection, and suffix h is added for the horizontal direction to expressthe magnification SM of an image, the above-described equations (1v′)and (1h′) are rewritten as follows:

SMv=Mpv×Msv×Mγv  (1v″)

SMh=Mph×Msh×Mγh  (1h″).

[0068] It should be noted that these Mγv and Mγh can be obtained in theprocess of the above-described accurate ray tracing calculations. Thiscan solve the problem of the influence by the prism action in themagnification calculations of a spectacle.

[0069] In a typical convex surface progressive-power lens, the distanceportion is lower than the near portion in surface refractive power of a“progressive surface” being the object side surface. In contrast tothis, in the progressive-power lens of Prior art 1, the distance portionis set equal to the near portion in surface refractive power of a“progressive surface” being the object side surface, thereby changingthe ratio in the shape factor between the distance and near portions anddecreasing the magnification difference between the distance and nearportions, so as to improve the distortion and sway of an image by theprogressive-power lens. In the study in the present invention, however,it is shown that although a reduction in the surface refractive powerdifference between the distance and near portions of a “progressivesurface” being the object side surface presents an advantage of adecrease in the magnification difference of an image between thedistance and near portions in the horizontal direction, there are someproblems in decreasing the surface refractive power difference in thevertical direction.

[0070] A first problem is influence by the prism factor Mγv in thevertical direction. The prism factor Mγv in the vertical direction is asMγv<1 when the near portion has a negative refractive power, and Mγv>1when the near portion has a positive refractive power as describedabove, and this tendency is enhanced by decreasing the surfacerefractive power difference in the vertical direction, whereby Mγvdeviates from Mγv=1, which is a magnification of a naked eye, in eithercase of the diopter in the near portion being positive or negative.Meanwhile, the prism factor Mγh in the horizontal direction receives nosuch influence, and thus it is kept as Mγh=1. As a result, there arisesa difference between the vertical and horizontal directions in themagnification of an image especially in a portion from the near portionto a portion lower than that, thereby causing a disadvantage that anitem which should look square under proper condition looks longer thanwider in a plus diopter and wider than longer in a minus diopter.

[0071] A second problem is one occurring only when the near portion hasa positive refractive power especially in the vertical direction.Specifically, when the surface refractive power difference in thevertical direction is decreased, the angle between the sight line andthe lens surface in the near vision is further increased, whereby thepower factor Mpv in the vertical direction is increased and acts doublywith the increase in the prism factor Mγv in the vertical direction,which is the first problem, to increase the magnification SMv in thevertical direction, resulting in a disadvantage that the magnificationdifference of an image between the distance and near portions increases.

[0072] In short, it is shown that the reduction in the surfacerefractive power difference between the distance and near portions of aprogressive surface being the object side surface is an advantage in thehorizontal direction but is conversely deterioration in the verticaldirection. Therefore, in a conventional-type convex surfaceprogressive-power lens, the above-described problems can be solved bydividing the progressive surface being the object side surface into thevertical direction and the horizontal direction, and decreasing thesurface refractive power difference between the distance and nearportions only in the horizontal direction.

[0073] These things completely apply to the fact that “the visual fieldis widened” which is generally regarded as a merit of rear surfaceprogression (or concave surface progression) as described below.

[0074] It is generally known that an excellent visual field in thehorizontal direction has its limits since there is astigmatism in theperipheral portion of the “progressive surface,” but if the “progressivesurface” is placed on the eyeball side surface, the “progressivesurface” itself approaches the eye to present an advantage that theexcellent visual filed is widened in the horizontal direction. On theother hand, this results in a further distance between the distance andnear visual regions in the vertical direction to present a disadvantagethat a labor increases in rotating the eye from the far vision to thenear vision. In other words, the rear surface progression (or concavesurface progression), as compared to the conventional front surfaceprogression (or convex surface progression), presents an advantage ofwidening the visual field in the horizontal direction but a disadvantageof increasing the rotating angle of the eye from the far vision to thenear vision in the vertical direction.

[0075] The present invention, however, includes the progressiverefracting surface which satisfies the relational equationsDHf+DHn<DVf+DVn and DHn<DVn, or DVn−DVf>ADD/2 and DHn−DHf<ADD/2 asdescribed above, and thus the present invention has characteristicscreated by the rear surface progression (or concave surface progression)greater than those by the conventional front surface progression (orconvex surface progression) in the horizontal direction, andcharacteristics created by the conventional front surface progression(or convex surface progression) greater than those by the rear surfaceprogression (or concave surface progression) in the vertical direction.Therefore, according to the present invention, it is possible torestrain the disadvantage of increasing the eyeball rotating anglebetween the distance and near portions in the vertical direction whilereceiving the advantage of increasing the visual field in the horizontaldirection.

[0076] Further, in an extreme example within the scope of the presentinvention, when DVn−DVf=ADD and DHn−DHf=0, a lens has progressionsidentical to the conventional front surface progression (or convexsurface progression) in the vertical direction and to the rear surfaceprogression (or concave surface progression) in the horizontaldirection. Therefore, this case presents an extremely excellent resultthat the advantage in the horizontal direction can be obtained withoutthe disadvantage in the vertical direction.

[0077] Further, these things also apply to decreasing the magnificationdifference of an image between the distance portion and the near portionand improving the distortion and sway of the image as described above,and thus they can be advantages of the present invention.

[0078] As has been described, the most important characteristic of thepresent invention is that a progressive action of a progressive-powerlens is divided in the vertical direction and the horizontal directionof the lens, and then an optimal sharing ratio between the front andrear two surfaces is set in each direction to configure onebi-aspherical type progressive-power lens. As an extreme example, it isalso within the scope of the present invention that all the progressiveaction in the vertical direction is provided by the object side surface,and all the progressive action in the horizontal direction is providedby the eyeball side surface. In this case, since either of the front andrear two faces does not function as a normal progressive surface only byone surface, the addition diopter as a progressive surface cannot bespecified. This results in a progressive-power lens having the front andrear surfaces both of which are not progressive surfaces. Contrarily,although the above-described various prior arts are different in sharingratio, in any of them the “value” of a required addition diopter isallotted to front and rear two surfaces, and after an actual progressivesurface to which each allotted addition diopter is given is imagined, acombined surface with a cylindrical surface is configured as required.Consequently, the point of the preset invention definitely differentfrom the prior arts exists in the configuration of a bi-aspherical typeprogressive-power lens using, on both surfarces, aspherical surfaceshaving progressive actions different depending on direction.

BRIEF DESCRIPTION OF DRAWINGS

[0079]FIG. 1 is an explanatory view of various surface refractive powersat positions on a spectacle lens;

[0080]FIG. 2 is an explanatory view of a positional relation among aneyeball, sight lines, and a lens surface;

[0081]FIG. 3-1 is an explanatory view on a magnification Mγ of a prism,being an explanatory view on a difference between a plus lens and aminus lens and on a difference in magnification in viewing mainly usinga near portion which is a lower portion of a lens;

[0082]FIG. 3-2 is an explanatory view on a magnification Mγ of a prism,being an explanatory view on a difference between a plus lens and aminus lens and on a difference in magnification in viewing mainly usinga near portion which is a lower portion of a lens;

[0083]FIG. 3-3 is an explanatory view on a magnification Mγ of a prism,being an explanatory view on a difference between a plus lens and aminus lens and on a difference in magnification in viewing mainly usinga near portion which is a lower portion of a lens;

[0084]FIG. 4-1 is an explanatory view on a magnification Mγ of a prism,being an explanatory view on a difference between a plus lens and aminus-lens and on a difference in magnifications in viewing mainly usinga near portion which is a lower portion of a lens;

[0085]FIG. 4-2 is an explanatory view on a magnification Mγ of a prism,being an explanatory view on a difference between a plus lens and aminus lens and on a difference in magnifications in viewing mainly usinga near portion which is a lower portion of a lens;

[0086]FIG. 4-3 is an explanatory view on a magnification Mγ of a prism,being an explanatory view on a difference between a plus lens and aminus lens and on a difference in magnifications in viewing mainly usinga near portion which is a lower portion of a lens;

[0087]FIG. 5-1 is an explanatory view of an optical layout of aprogressive-power lens, being a front view of the progressive power lenswhen viewed from an object side surface;

[0088]FIG. 5-2 is an explanatory view of the optical layout of theprogressive-power lens, being a side view illustrating a cross sectionin the vertical direction;

[0089]FIG. 5-3 is an explanatory view of the optical layout of theprogressive-power lens, being an elevational view illustrating a crosssection in the transverse direction;

[0090]FIG. 6 is an explanatory view illustrating the difference ofdefinition on “addition diopter”;

[0091]FIG. 7 is a view collectively showing in Table 1-1 and Table 1-2“surface refractive powers” and “results of accurate magnificationcalculations in a direction of a specific sight line” of Examples 1, 4,5, and 6 and Prior arts A, B, and C corresponding to the diopters ofExamples 1, 4, 5, and 6;

[0092]FIG. 8 is a view collectively showing in Table 2-1 and Table 2-2“surface refractive powers” and “results of accurate magnificationcalculations in a direction of a specific sight line” of Examples 2 and7 and Prior arts A, B, and C corresponding to the diopters of Examples 2and 7;

[0093]FIG. 9 is a view collectively showing in Table 3-1 and Table 3-2“surface refractive powers” and “results of accurate magnificationcalculations in a direction of a specific sight line” of Example 3 andPrior arts A, B, and C corresponding to the diopters of the example 3;

[0094]FIG. 10 is a view showing Graphs 1-1, 1-2, 2-1, and 2-2representing the surface refractive power distributions of Example 1 andExample 2;

[0095]FIG. 11 is a view showing Graphs 3-1 and 3-2 representing thesurface refractive power distributions of Example 3;

[0096]FIG. 12 is a view showing Graphs 4-1, 4-2, 5-1, 5-2, 6-1 and 6-2representing the surface refractive power distributions of Example 4 toExample 6;

[0097]FIG. 13 is a view showing Graphs 7-1 and 7-2 representing thesurface refractive power distributions of Example 7;

[0098]FIG. 14 is a view showing Graphs A-1, A-2, B-1, B-2, C-1 and C-2representing the surface refractive power distributions of Prior artexamples A, B, and C;

[0099]FIG. 15 is a view showing Graph 1-3-Msv representing results,obtained by performing accurate magnification calculations, ofmagnification distributions when lenses of Example 1 and three kinds ofPrior art examples A, B, and C corresponding to the diopters of Example1 are viewed along main gazing lines;

[0100]FIG. 16 is a view showing Graph 1-3-Msh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 1 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 1 are viewed along the main gazing lines;

[0101]FIG. 17 is a view showing Graph 1-3-Mpv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 1 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 1 are viewed along the main gazing lines;

[0102]FIG. 18 is a view showing Graph 1-3-Mph representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 1 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 1 are viewed along the main gazing lines;

[0103]FIG. 19 is a view showing Graph 1-3-Mγv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 1 and the threekinds of Prior art examples A, B, and C corresponding to the diopter ofExample 1 are viewed along the main gazing lines;

[0104]FIG. 20 is a view showing Graph 1-3-Mγh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 1 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 1 are viewed along the main gazing lines;

[0105]FIG. 21 is a view showing Graph 1-3-SMv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 1 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 1 are viewed along the main gazing lines;

[0106]FIG. 22 is a view showing Graph 1-3-SMh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 1 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 1 are viewed along the main gazing lines;

[0107]FIG. 23 is a view showing Graph 2-3-Msv representing results,obtained by performing accurate magnification calculations, ofmagnification distributions when lenses of Example 2 and three kinds ofPrior art examples A, B, and C corresponding to the diopters of Example2 are viewed along main gazing lines;

[0108]FIG. 24 is a view showing Graph 2-3-Msh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 2 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 2 are viewed along the main gazing lines;

[0109]FIG. 25 is a view showing Graph 2-3-Mpv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 2 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 2 are viewed along the main gazing lines;

[0110]FIG. 26 is a view showing Graph 2-3-Mph representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 2 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 2 are viewed along the main gazing lines;

[0111]FIG. 27 is a view showing Graph 2-3-Mγv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 2 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 2 are viewed along the main gazing lines;

[0112]FIG. 28 is a view showing Graph 2-3-Mγh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 2 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 2 are viewed along the main gazing lines;

[0113]FIG. 29 is a view showing Graph 2-3-SMv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 2 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 2 are viewed along the main gazing lines;

[0114]FIG. 30 is a view showing Graph 2-3-SMh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 2 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 2 are viewed along the main gazing lines;

[0115]FIG. 31 is a view showing Graph 3-3-Msv representing results,obtained by performing accurate magnification calculations, ofmagnification distributions when lenses of Example 3 and three kinds ofPrior art examples A, B, and C corresponding to the diopters of Example3 are viewed along main gazing lines;

[0116]FIG. 32 is a view showing Graph 3-3-Msh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 3 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 3 are viewed along the main gazing lines;

[0117]FIG. 33 is a view showing Graph 3-3-Mpv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 3 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 3 are viewed along the main gazing lines;

[0118]FIG. 34 is a view showing Graph 3-3-Mph representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 3 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 3 are viewed along the main gazing lines;

[0119]FIG. 35 is a view showing Graph 3-3-Mγv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 3 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 3 are viewed along the main gazing lines;

[0120]FIG. 36 is a view showing Graph 3-3-Mγh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 3 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 3 are viewed along the main gazing lines;

[0121]FIG. 37 is a view showing Graph 3-3-SMv representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 3 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 3 are viewed along the main gazing lines; and

[0122]FIG. 38 is a view showing Graph 3-3-SMh representing results,obtained by performing accurate magnification calculations, of themagnification distributions when the lenses of Example 3 and the threekinds of Prior art examples A, B, and C corresponding to the diopters ofExample 3 are viewed along the main gazing lines.

BEST MODE FOR CARRYING OUT THE INVENTION

[0123] Hereinafter, a bi-aspherical type progressive-power lensaccording to an embodiment of the present invention of the applicationwill be described. In the following description, a designing method usedfor obtaining the bi-aspherical type progressive-power lens according tothe embodiment will be described first, and then the bi-aspherical typeprogressive-power lens according to the embodiment will be described.

Procedures of Lens Design

[0124] The outline of procedures of an optical designing method of thebi-aspherical type progressive-power lens according to the embodiment isas follows:

[0125] {circle over (1)} Setting of input information,

[0126] {circle over (2)} Double surface design as a convexprogressive-power lens,

[0127] {circle over (3)} Conversion into a convex surface shape of thepresent invention and accompanying rear surface correction, and

[0128] {circle over (4)} Rear surface correction accompanying atransmission design, a Listing's law-compliant design, and so on.Hereinafter, the individual procedure will be made into further dividedsteps for detailed description.

[0129] {circle over (1)} Setting of Input Information

[0130] The input information is roughly divided into the following twokinds (information other than optical design is omitted).

[0131] {circle over (1)}-1: Item Specific Information

[0132] Data specific to a lens item. A refractive index of a rawmaterial Ne, a minimum center thickness CTmin, a minimum edge thicknessETmin, progressive surface design parameters, and so on.

[0133] {circle over (1)}-2: Wearer Specific Information

[0134] A far vision diopter (a spherical surface diopter S, acylindrical diopter C, a cylindrical axis AX, a prism diopter P, a prismbase direction PAX, and so on), an addition diopter ADD, frame shapedata (preferably, three-dimensional shape data), frame wearing data (aforward tilt angle, a horizontal tilt angle, and so on), an inter-vertexdistance, lay-out data (a far vision PD, a near vision CD, an eye pointposition, and so on), and other data on an eyeball. It should be notedthat progressive surface design parameters such as a progressive zonelength specified by a wearer, a measuring method of an addition diopter,an amount of inner shift of the near portion are classified into thewearer specific information.

[0135] {circle over (2)} Double Surface Design as a ConvexProgressive-power Lens

[0136] A lens is first designed, divided into a convex surface and aconcave surface, as a conventional type convex progressive-power lens.

[0137] {circle over (2)}-1: Convex Surface Shape (Convex ProgressiveSurface) Design

[0138] To realize the addition diopter ADD and the progressive zonelength provided as input information, a conventional type convexprogressive surface shape is designed in accordance with the progressivesurface design parameters being the input information. Variousconventional known technologies can be used in the design in this step,and thus the design technology of the present invention is unnecessary.

[0139] A specific example of this method is, for example, a method ofsetting first a “main meridian” corresponding to a spine when forming alens surface. It is preferable that the “main meridian” is finally a“main gazing line” corresponding to an intersecting line of a sight lineand a lens surface when a spectacle wearer looks with both eyes from afront upper portion (far) to a lower portion (near). However, the innershift of the near region in response to the convergence action of theeye in the near vision is not necessarily dealt with through inner shiftof the “main gazing line” as will be described later. Therefore, the“main gazing line” here is defined as one meridian (main meridian) inthe vertical direction which passes through the lens center and dividesthe lens surface into a right part and a left part. A lens has front andrear two surfaces, and thus there are two “main meridians” on the frontand rear surfaces. The “main meridian” looks straight when viewedperpendicularly to the lens surface, but it generally becomes a curvedline in a three-dimensional space when the lens surface is a curvedsurface.

[0140] Then, based on the information such as a predetermined additiondiopter and progressive zone length, an appropriate refractive powerdistribution along the “main meridian” is set. Although the refractivepower distribution can be set dividedly to the front and rear twosurfaces, with the influence by the thickness of the lens and an anglebetween a sight line and a refractive surface taken into consideration,all the progressive action should be provided on a first refractivesurface being an object side surface since the conventional type convexprogressive surface shape is designed in this step. Therefore, forexample, assuming that when a surface refractive power of a frontsurface (a first refractive surface being an object side surface) of alens is D1, and a surface refractive power of a rear surface (a secondrefractive surface being an eyeball side surface) of the lens is D2, aresulting transmission refractive power is D, generally the transmissionrefractive power D can be approximately obtained as D≈D1−D2. Thecombination of D1 and D2, however, preferably has a meniscus shape inwhich the object side surface is convex and the eyeball side surface isconcave. Note that D2 has a positive value here. Although the rearsurface of the lens is generally a concave surface and thus has asurface refractive power of a negative value, D2 should be given apositive value in this specification for simplification of descriptionto calculate the transmission refractive power D by subtracting D2 fromD1.

[0141] A relational equation between the surface refractive power andthe surface shape is generally defined by the following equation,

Dn=(N−1)/R

[0142] where Dn: a surface refractive power of an n-th surface (unit:diopter), N: a refractive index of a lens material, R: a radius ofcurvature (unit: m). Therefore, a method of converting the distributionof the surface refractive power into a distribution of curvature usesthe equation,

1/R=Dn/(N−1),

[0143] created by transforming the above relational equation. Byobtaining the distribution of curvature, the geometrical shape of the“main meridian” is uniquely determined, which means that the “mainmeridian” corresponding to the spine in forming a lens surface is set.

[0144] What is required next is a “sectional curved line group in thehorizontal direction” corresponding to costae in forming the lenssurface. Though intersecting angles of the “sectional curved line groupin the horizontal direction” and the “main meridian” are not necessarilyright angles, each “sectional curved line in the horizontal direction”should intersect at right angles with the “main meridian” to simplifythe description Further, “surface refractive powers in the horizontaldirection” of the “sectional curved line group in the horizontaldirection” at intersections with the “main meridian” do not always needto be identical to “surface refractive powers in the vertical direction”along the “main meridian”, and the present invention is made based onthe difference in the surface refractive power between the verticaldirection and the horizontal direction as actually described in claims.In the design in this step, however, since the conventional type convexprogressive surface shape is designed, the surface refractive powers inthe vertical direction and the horizontal direction at the intersectionsshould be identical with each other.

[0145] By the way, all the “sectional curved lines in the horizontaldirection” can be simple circular curved lines having surface refractivepowers at the intersections, and can also be made with applications byvarious prior arts incorporated thereto. One of conventionaltechnologies on surface refractive power distribution along the“sectional curved line in the horizontal direction” is, for example, atechnology in Japanese Patent Publication No. Sho 49-3595. Thistechnology is characterized in that one “sectional curved lines in thehorizontal direction” in an almost circular shape is set near the centerof a lens, and sectional curved lines positioned at an upper portion ismade to have a distribution of surface refractive power increasing fromthe center to the side, and sectional curved lines positioned at a lowerportion is made to have a distribution of surface refractive powerdecreasing from the center to the side. As described above, the “mainmeridian” and the “sectional curved line group in the horizontaldirection” composed of an uncountable number of lines positioned side byside thereon, form a lens surface as the spine and costae, thusdetermining a refractive surface.

[0146] {circle over (2)}-2: Concave Surface Shape (Spherical orCylindrical Surface) Design

[0147] To realize the far vision diopter provided as the inputinformation, a concave surface shape is designed. The surface becomes acylindrical surface if the far vision diopter includes a cylindricaldiopter, and a spherical surface if not. In this event, the centerthickness CT suitable for the diopter and the tilt angle betweensurfaces, the convex surface and the concave surface, are also designedat the same time, thus determining the shape as a lens. Variousconventional known technologies can also be used in the design in thisstep, and thus the design technology of the present invention isunnecessary.

[0148] {circle over (3)} Conversion into a Convex Shape of the PresentInvention and Accompanying Rear Surface Correction

[0149] In accordance with the far vision diopter and the additiondiopter ADD provided as the input information, the conventional typeconvex progressive-power lens is converted into the shape as a lens ofthe present invention.

[0150] {circle over (3)}-1: Convex Surface Shape (the Present Invention)Design

[0151] In accordance with the far vision diopter and the additiondiopter ADD provided as the input information, the conventional typeconvex progressive surface is converted into the convex surface shape ofthe present invention. More specifically, when a surface refractivepower in the horizontal direction and a surface refractive power in thevertical direction, at a far vision diopter measurement position F1, areDHf and DVf respectively, and a surface refractive power in thehorizontal direction and a surface refractive power in the verticaldirection, at a near vision diopter measurement position N1, are DHn andDVn respectively, the above-described conventional convex progressivelens surface (the first refractive surface being the object sidesurface) is converted into a progressive refracting surface whichsatisfies the relational equations,

DHf+DHn<DVf+DVn, and DHn<DVn,

[0152] or the relational equations,

DVn−DVf>ADD/2, and DHn−DHf<ADD/2.

[0153] In this event, the shape is preferably converted into the convexsurface shape of the present invention without changing the averagesurface refractive power of the whole convex surface. It is conceivable,for example, to keep the total average value of the surface refractivepowers in the vertical and horizontal directions in the distance portionand the near portion. The value, however, desirably falls within a rangekeeping a meniscus shape in which the object side surface is convex andthe eyeball side surface is concave.

[0154] {circle over (3)}-2: Concave Surface Shape (the PresentInvention) Design

[0155] The amount of transformation in converting from the conventionaltype convex progressive surface into the convex surface shape of thepresent invention in the above-described {circle over (3)}-1, is addedto the concave surface shape designed in {circle over (2)}-2. In otherwords, the amount of transformation, identical to that of the frontsurface (the first refractive surface being the object side surface) ofthe lens added in the process {circle over (3)}-1, is added to the rearsurface (the second refractive surface being the eyeball side surface)of the lens. Note that this transformation is not uniform over the wholesurface though it is similar to “bending” in which the lens itself isbent, but makes a surface which satisfies the relational equationsdescribed in {circle over (3)}-1. It should be noted that the rearsurface corrections are within the scope of the present invention, butare merely corrections of linear approximation, and it is preferable toadd rear surface correction in {circle over (4)}.

[0156] {circle over (4)} Rear surface correction accompanyingtransmission design, a Listing's law-compliant design, design for aninner shift-compliant design of a near portion, and so on

[0157] To realize the optical function provided as the inputinformation, in a situation in which a wearer actually wears a lens, itis desirable to further add rear surface correction to the lens of thepresent invention obtained in {circle over (3)}.

[0158] {circle over (4)}-1: Concave Surface Shape (the PresentInvention) Design for Transmission Design

[0159] The transmission design means a designing method for obtaining anessential optical function in the situation in which a wearer actuallywears a lens, a designing method of adding a “correction action” foreliminating or reducing occurrence of astigmatism and change in diopterprimarily caused by impossibility of a sight line intersecting at rightangles with a lens surface.

[0160] Specifically, as described above, the difference of opticalperformance of the lens with respect to a target essential opticalperformance is grasped through accurate ray tracing calculation inaccordance with the direction of the sight line, and surface correctionto cancel the difference is implemented. By repeating this, thedifference can be minimized to obtain an optimal solution. Generally, itis often very difficult and actually impossible to directly calculate alens shape having a target optical performance. This is because a “lensshape having an arbitrarily set optical performance” does not alwaysactually exist. Conversely, it is relatively easy to obtain an “opticalperformance of an arbitrarily set lens shape.” Therefore, it is possibleto bring the optical performance to a target optical performance byfirst provisionally calculating a linearly approximated surface by anarbitrary method, finely adjusting the design parameters in accordancewith evaluation results on the optical performance of the lens shapeusing the approximated surface to sequentially modulate the lens shape,and returning to the evaluation step for a repeat of reevaluation andreadjustment. This technique is one of well-known techniques called“optimization.”

[0161] {circle over (4)}-2: Concave Surface Shape (the PresentInvention) Design for a Listing's Law-compliant Design

[0162] It is known that three-dimensional rotating motions of eyes whenwe look around are based on a rule called “Listing's law.” When aprescription diopter includes a cylindrical diopter, cylindrical axes ofa spectacle lens and the eye may not match to each other in peripheralvision even if the cylindrical axis of the lens is matched to the“cylindrical axis of the eye in front vision.” It is also possible toadd a “correction action” for eliminating or reducing occurrence ofastigmatism and change in diopter caused by such a mismatch between thecylindrical axes of the lens and the eye in the peripheral vision, to acurved surface being the surface on the side having a cylindricalcorrection action of a lens according to the present invention.

[0163] Specifically, similarly to the method of the “optimization” usedin {circle over (4)}-1, the difference of optical performance of thelens with respect to a target essential optical performance is graspedthrough accurate ray tracing calculation in accordance with thedirection of the sight line, and surface correction to cancel thedifference is implemented. By repeating this, the difference can beminimized to obtain an optimal solution.

[0164] {circle over (4)}-3: Concave Surface Shape (the PresentInvention) Design for an Inner Shift-compliant Design of a Near Portion

[0165] Though the present invention is of a surface configuration beinga bi-aspherical surface, both surfaces are not always processed afteracceptance of an order to obtain an effect of the present invention. Itis advantageous in terms of cost and processing speed, for example, toprepare in advance “semifinished products” of the object side surfacemeeting the object of the present invention, select, after acceptance ofan order, from among them a “semifinished product” of the object sidesurface meeting the purpose such as a prescription diopter or theabove-described custom-made product (individual design), and process andfinish only the eyeball side surface after the acceptance of the order.

[0166] In a specific example of this method, the object side surface isprepared in advance as a bilaterally symmetrical “semifinished product”in the above-described convex surface shape (the present invention)design in {circle over (3)}-1, and the eyeball side surface is designedas a bilaterally asymmetrical curved surface meeting the purpose afterbeing inputted individual information such as an inter-pupil distance,object distance in near vision, whereby the inner shift of the nearportion in response to the individual information can be performed.

[0167] Hereinafter, examples of the bi-aspherical surface progressiverefractive lens designed by the above-described designing method will bedescribed with reference to the drawings. FIG. 7 is a view collectivelyshowing in Table 1-1 and Table 1-2 “surface refractive powers” and“results of accurate magnification calculations in a direction of aspecific sight line” of Examples 1, 4, 5, and 6 and Prior arts A, B, andC corresponding to the diopters of Examples 1, 4, 5, and 6. FIG. 8 is aview collectively showing in Table 2-1 and Table 2-2 “surface refractivepowers” and “results of accurate magnification calculations in adirection of a specific sight line” of Examples 2 and 7 and Prior artsA, B, and C corresponding to the diopters of Examples 2 and 7. FIG. 9 isa view collectively showing in Table 3-1 and Table 3-2 “surfacerefractive powers” and “results of accurate magnification calculationsin a direction of a specific sight line” of Example 3 and Prior arts A,B, and C corresponding to the diopters of the example 3. FIG. 10 is aview showing Graphs 1-1, 1-2, 2-1, and 2-2 representing the surfacerefractive power distributions of Example 1 and Example 2, FIG. 11 is aview showing Graphs 3-1 and 3-2 representing the surface refractivepower distributions of Example 3, FIG. 12 is a view showing Graphs 4-1,4-2, 5-1, 5-2, 6-1 and 6-2 representing the surface refractive powerdistributions of Example 4 to Example 6, FIG. 13 is a view showingGraphs 7-1 and 7-2 representing the surface refractive powerdistributions of Example 7, and FIG. 14 is a view showing Graphs A-1,A-2, B-1, B-2, C-1 and C-2 representing the surface refractive powerdistributions of Prior art examples A, B, and C.

[0168]FIG. 15 is a view showing Graph 1-3-Msv representing the results,obtained by performing accurate magnification calculations, ofmagnification distributions when lenses of Example 1 and three kinds ofPrior art examples A, B, and C corresponding to the diopters of Example1 are viewed along main gazing lines, FIG. 16 is a view showing Graph1-3-Msh representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 1 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 1 are viewed along the maingazing lines, FIG. 17 is a view showing Graph 1-3-Mpv representingresults, obtained by performing accurate magnification calculations, ofthe magnification distributions when the lenses of Example 1 and thethree kinds of Prior art examples A, B, and C corresponding to thediopters of Example 1 are viewed along the main gazing lines, FIG. 18 isa view showing Graph 1-3-Mph representing results, obtained byperforming accurate magnification calculations, of the magnificationdistributions when the lenses of Example 1 and the three kinds of Priorart examples A, B, and C corresponding to the diopters of Example 1 areviewed along the main gazing lines, FIG. 19 is a view showing Graph1-3-Mγv representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 1 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 1 are viewed along the maingazing lines, FIG. 20 is a view showing Graph 1-3-Mγh representingresults, obtained by performing accurate magnification calculations, ofthe magnification distributions when the lenses of Example 1 and thethree kinds of Prior art examples A, B, and C corresponding to thediopters of Example 1 are viewed along the main gazing lines, FIG. 21 isa view showing Graph 1-3-SMv representing results, obtained byperforming accurate magnification calculations, of the magnificationdistributions when the lenses of Example 1 and the three kinds of Priorart examples A, B, and C corresponding to the diopters of Example 1 areviewed along the main gazing lines, and FIG. 22 is a view showing Graph1-3-SMh-representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 1 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 1 are viewed along the maingazing lines.

[0169]FIG. 23 is a view showing Graph 2-3-Msv representing results,obtained by performing accurate magnification calculations, ofmagnification distributions when lenses of Example 2 and three kinds ofPrior art examples A, B, and C corresponding to the diopters of Example2 are viewed along main gazing lines, FIG. 24 is a view showing Graph2-3-Msh representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 2 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 2 are viewed along the maingazing lines, FIG. 25 is a view showing Graph 2-3-Mpv representingresults, obtained by performing accurate magnification calculations, ofthe magnification distributions when the lenses of Example 2 and thethree kinds of Prior art examples A, B, and C corresponding to thediopters of Example 2 are viewed along the main gazing lines, FIG. 26 isa view showing Graph 2-3-Mph representing results, obtained byperforming accurate magnification calculations, of the magnificationdistributions when the lenses of Example 2 and the three kinds of Priorart examples A, B, and C corresponding to the diopters of Example 2 areviewed along the main gazing lines, FIG. 27 is a view showing Graph2-3-Mγv representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 2 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 2 are viewed along-the maingazing lines, FIG. 28 is a view showing Graph 2-3-Mγh representingresults, obtained by performing accurate magnification calculations, ofthe magnification distributions when the lenses of Example 2 and thethree kinds of Prior art examples A, B, and C corresponding to thediopters of Example 2 are viewed along the main gazing lines, FIG. 29 isa view showing Graph 2-3-SMv representing results, obtained byperforming accurate magnification calculations, of the magnificationdistributions when the lenses of Example 2 and the three kinds of Priorart examples A, B, and C corresponding to the diopters of Example 2 areviewed along the main gazing lines, and FIG. 30 is a view showing Graph2-3-SMh representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 2 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 2 are viewed along the maingazing lines.

[0170]FIG. 31 is a view showing Graph 3-3-Msv representing results,obtained by performing accurate magnification calculations, ofmagnification distributions when lenses of Example 3 and three kinds ofPrior art examples A, B, and C corresponding to the diopters of Example3 are viewed along main gazing lines, FIG. 32 is a view showing Graph3-3-Msh representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 3 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 3 are viewed along the maingazing lines, FIG. 33 is a view showing Graph 3-3-Mpv representingresults, obtained by performing accurate magnification calculations, ofthe magnification distributions when the lenses of Example 3 and thethree kinds of Prior art examples A, B, and C corresponding to thediopters of Example 3 are viewed along the main gazing lines, FIG. 34 isa view showing Graph 3-3-Mph representing results, obtained byperforming accurate magnification calculations, of the magnificationdistributions when the lenses of Example 3 and the three kinds of Priorart examples A, B, and C corresponding to the diopters of Example 3 areviewed along the main gazing lines, FIG. 35 is a view showing Graph3-3-Mγv representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 3 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 3 are viewed along the maingazing lines, FIG. 36 is a view showing Graph 3-3-Mγh representingresults, obtained by performing accurate magnification calculations, ofthe magnification distributions when the lenses of Example 3 and thethree kinds of Prior art examples A, B, and C corresponding to thediopters of Example 3 are viewed along the main gazing lines, FIG. 37 isa view showing Graph 3-3-SMv representing results, obtained byperforming accurate magnification calculations, of the magnificationdistributions when the lenses of Example 3 and the three kinds of Priorart examples A, B, and C corresponding to the diopters of Example 3 areviewed along the main gazing lines, and FIG. 38 is a view showing Graph3-3-SMh representing results, obtained by performing accuratemagnification calculations, of the magnification distributions when thelenses of Example 3 and the three kinds of Prior art examples A, B, andC corresponding to the diopters of Example 3 are viewed along the maingazing lines.

EXAMPLE 1

[0171] Table 1-1 in FIG. 7 is a list regarding the surface refractivepowers of Example 1 according to the present invention. The diopters ofExample 1 correspond to S being 0.00 and ADD being 3.00, with threekinds of prior art examples having the same diopters being listedtogether for comparison. It should be noted that Prior art example A,Prior art example B, and Prior art example C correspond to a “convexsurface progressive-power lens” in which the object side surface is aprogressive surface, a “bi-surface progressive-power lens” in which boththe object side surface and eyeball side surface are progressivesurfaces, and a “concave surface progressive-power lens” in which theeyeball side surface is a progressive surface, respectively. Meanings ofitems used in Table 1-1 are as follows:

[0172] DVf1: surface refractive power in the vertical direction at a farvision diopter measurement position F1 on the object side surface,

[0173] DHf1: surface refractive power in the horizontal direction at thefar vision diopter measurement position F1 on the object side surface,

[0174] DVn1: surface refractive power in the vertical direction at anear vision diopter measurement position N1 on the object side surface,

[0175] DHn1: surface refractive power in the horizontal direction at thenear vision diopter measurement position N1 on the object side surface,

[0176] DVf2: surface refractive power in the vertical direction at a farvision diopter measurement position F2 on the eyeball side surface,

[0177] DHf2: surface refractive power in the horizontal direction at thefar vision diopter measurement position F2 on the eyeball side surface,

[0178] DVn2: surface refractive power in the vertical direction at anear vision diopter measurement position N2 on the eyeball side surface,and

[0179] DHn2: surface refractive power in the horizontal direction at thenear vision diopter measurement position N2 on the eyeball side surface.

[0180] Graphs 1-1 and 1-2 in FIG. 10 are graphs showing the surfacerefractive power distributions along the main gazing lines of Example 1,with the horizontal axis indicating the lens upper side on the righthand side and the lens lower side on the left hand side, and thevertical axis indicating the surface refractive power. Here, Graph 1-1corresponds to the object side surface, and Graph 1-2 corresponds to theeyeball side surface. Besides, the graph shown by a solid linerepresents the surface refractive power distribution in the verticaldirection along the main gazing line, and the graph shown by a dottedline represents the surface refractive power distribution in thehorizontal direction along the main gazing line. It should be noted thatthese are graphs for explaining the basic difference in surfaceconfiguration, omitting a case of aspherical processing for eliminatingastigmatism in a peripheral portion and a case of addition of acylindrical component for coping with a cylindrical diopter.

[0181] Further, for comparison, Graphs A-1 and A-2, Graphs B-1 and B-2,and Graphs C-1 and C-2 are shown in FIG. 14 as graphs showing thesurface refractive power distributions along the main gazing lines ofthe three kinds of prior art examples having the same diopters, whichare listed in Table 1-1. Note that, meanings of terms in these graphsare as follows:

[0182] F1: far vision diopter measurement position on the object sidesurface,

[0183] F2: far vision diopter measurement position on the eyeball sidesurface,

[0184] N1: near vision diopter measurement position on the object sidesurface,

[0185] N2: near vision diopter measurement position on the eyeball sidesurface,

[0186] CV1: graph showing the surface refractive power distribution inthe vertical direction along the main gazing line on the object sidesurface (shown by the solid line),

[0187] CH1: graph showing the surface refractive power distribution inthe horizontal direction along the main gazing line on the object sidesurface (shown by the dotted line),

[0188] CV2: graph showing the surface refractive power distribution inthe vertical direction along the main gazing line on the eyeball sidesurface (shown by the solid line), and

[0189] CH2: graph showing the surface refractive power distribution inthe horizontal direction along the main gazing line on the eyeball sidesurface (shown by the dotted line).

[0190] The surface refractive powers at F1, N1, F2, and N2 on thesegraphs correspond to those in the aforementioned Table 1-1, and meaningsof the terms such as DVf1 to DHn2 are also the same as those in theaforementioned Table 1-1. Note that one-dotted chain lines in thehorizontal direction at the middle in these graphs show average surfacerefractive powers on the object side surface (total average values ofthe vertical and horizontal surface refractive powers at F1 and N1). Anyof the average surface refractive powers on the object side surface inExample 1 according to the present invention and the three kinds ofprior art examples was uniformly set to 5.50 diopter for fairness incomparison.

[0191] The next eight kinds of graphs starting with Graph 1-3-shown inFIG. 15 to FIG. 22 are graphs showing results, obtained by performingthe above-described accurate magnification calculations, ofmagnification distributions when the lens of Example 1 according to thepresent invention is viewed along the main gazing line, with thehorizontal axis indicating the lens upper side on the right hand sideand the lens left lower side on the left hand side, and the verticalaxis indicating the magnification. In the drawing, a thick solid line isfor Example 1, a thin chain line is for Prior art example A, a thickchain line is for Prior art example B, and a thin solid line is forPrior art example C. These apply to the following graphs of this kind.Note that the horizontal axis was set to allow comparison for each sightline direction through use of eyeball rotating angles, and magnificationscales on the vertical axes of the graphs were matched to each other forfairness. Symbols appended to “Graph 1-3-” mean,

[0192] Msv: shape factor in the vertical direction,

[0193] Msh: shape factor in the horizontal direction,

[0194] Mpv: power factor in the vertical direction,

[0195] Mph: power factor in the horizontal direction,

[0196] Mγv: prism factor in the vertical direction,

[0197] Mγh: prism factor in the horizontal direction,

[0198] SMv: magnification in the vertical direction, and

[0199] SMh: magnification in the horizontal direction,

[0200] and, as described above, the magnification SMv in the verticaldirection and the magnification SMh in the horizontal direction are inthe relation such that

SMv=Msv×Mpv×Mγv

SMh=Msh×Mph×Mγh.

[0201] It should be noted that any of Example 1 and the above-describedthree kinds of prior art examples was made under specifications with therefractive index n=1.699, the center thickness t=3.0 mm, and no prism atthe geometrical center GC. The objective power (inverse number of theobject distance) was set such that the objective power Px at F1, F2 wasset as Px=0.00 diopter (infinite far), the objective power Px at N1, N2was set as Px=2.50 diopter (40 cm), and the objective powers given inother positions were made by multiplying ratios of the additionalrefractive powers along the main gazing line by 2.50 diopter. Besides,the distance L from the lens rear vertex to the corneal vertex was setas L=15.0 mm, and the distance from the corneal vertex to the eyeballtuning center CR was set as CR=13.0 mm. The eyeball rotating angle θ wasindicated, with the eyeball tuning center point C being positioned onthe normal line passing through the geometrical center GC on the objectside lens surface, the rotating angle when the normal line and the sightline match to each other being regarded as 0 degree, and the upperportion shown with (+) and the lower portion shown with (−). Thereafter,standardization was made such that the eyeball rotating angle θ withrespect to F1, F2 was +30.0 degrees, and the eyeball rotating angle θwith respect to N1, N2 was −15.0 degrees, for consideration of allowingcomparison on the same condition even the progressive action and thesurface refractive power distribution were either on front or rear side.

[0202] Table 1-2 in FIG. 7 is a list of results obtained by performingthe above-described accurate magnification calculations for a specificsight line direction of Example 1 according to the present invention andthe three kinds of prior art examples prepared for comparison, andcorresponds to the above-described Graph 1-3-SMv (total magnification inthe vertical direction) in FIG. 21 and Graph 1-3-SMh (totalmagnification in the horizontal direction) in FIG. 22. Sincemagnification values are different between the vertical direction andhorizontal direction as described above, both magnifications werecalculated. Here, meanings represented by symbols in Table 1-2 are asfollows:

[0203] SMvf: magnification in the vertical direction on a sight linepassing through a far vision measurement point,

[0204] SMvn: magnification in the vertical direction on a sight linepassing through a near vision measurement point,

[0205] SMvfn: magnification difference in the vertical direction(SMvn−SMvf),

[0206] SMhf: magnification in the horizontal direction on a sight linepassing through a far vision measurement point,

[0207] SMhn: magnification in the horizontal direction on a sight linepassing through a near vision measurement point, and

[0208] SMhfn: magnification difference in the horizontal direction(SMhn−SMhf).

[0209] SMvfn and SMhfn in Table 1-2, that is, the magnificationdifference in the vertical direction (SMvn−SMvf) and the magnificationdifference in the horizontal direction (SMhn−SMhf), show that the valuesof magnification differences of Example 1 according to the presentinvention are suppressed to as low as 0.1342 and 0.0954, whereas thoseof the prior art examples are 0.1380 and 0.1015 in A, 0.1360 and 0.0988in B, and 0.1342 and 0.0961 in C. In other words, the magnificationdifference between the distance portion and the near portion of Example1 according to the present invention are made further smaller than thoseof Prior art 1, which shows that Example 1 is improved more greatly thanPrior art 1 also in distortion and sway of an image. Note that thedifference between the vertical direction and the horizontal directionin calculating the magnification is not taken into consideration at allin the patent specification corresponding to the above-described Priorart 1. However, as is immediately apparent from comparison between Graph1-3-SMv (total magnification in the vertical direction) in FIG. 21 andGraph 1-3-SMh in FIG. 22 (total magnification in the horizontaldirection) resulting from accurate magnification calculations,corresponding to Example 1 according to the present invention,magnification distributions of an image in the vertical direction andthe horizontal direction are apparently different. Further, it is easilyread that this difference is prominent mainly in the near portion and aportion lower than that (at an eyeball rotating angle of around −20degrees and lower).

[0210] As expressed in the above-described magnification calculationequations,

the magnification in the vertical direction SMv=Msv×Mpv×Mγv,

the magnification in the horizontal direction SMh=Msh×Mph×Mγh,

[0211] Graph 1-3-SMv is obtained by multiplying three elements, that is,values of Graph 1-3-Msv, Graph 1-3-Mpv, and Graph 1-3-Mγv, and similarlyGraph 1-3-SMh is obtained by multiplying three elements, that is, valuesof Graph 1-3-Msh, Graph 1-3-Mph, and Graph 1-3-Mγh. In comparisonbetween the elements in the vertical direction and the horizontaldirection here, there is no apparent difference found between Msv andMsv which are shape factors, whereas there is a difference found betweenMpv and Mph in a portion lower than the near portion (at an eyeballrotating angle of around −25 degrees and lower). Further, there is anobvious difference between Mγv and Mγh in the near portion and a lowerportion than that (at an eyeball rotating angle of around −15 degreesand lower). In short, it is shown that the major cause of the differencebetween Graph 1-3-SMv and Graph 1-3-SMh is the difference between Mγvand Mγh, the secondary cause thereof is the difference between Mpv andMph, and there is no obvious difference found between Msv and Msh, whichare almost irrelevant thereto. Consequently, the reason why there is nodifference found between magnifications in the vertical direction andthe horizontal direction in the patent specification corresponding toPrior art 1 is that the prism factors Mγv and Mγh, which are majorcauses of a magnification difference, are not taken into considerationat all, and because the object distance and the angle between the sightline and lens are neglected, there is no difference found between thepower factors Mpv and Mph, which are secondary causes. Further, there isno difference found among the examples in the magnification differencebetween the distance portion and the near portion, as long as in thescale used in Example 1 of the present invention, in the shape factorsMsv and Msh which are regarded as reasons of improvement in Prior art 1.

[0212] In Prior art 1 “the distortion and sway of an image can bereduced” by “decreasing the magnification difference between thedistance portion and the near portion,” and further “decreasing themagnification difference between the vertical direction and thehorizontal direction” is also regarded as having an effect of “capableof reducing the distortion and sway of an image” in the presentinvention. This is intended to prevent a square item from looking flat,or a circular item from looking oval. The improvement in visual sensewould be essentially seen as “bringing the ratio closer to 1” ratherthan “reducing the difference.” What is important here is that the senseof a square item looking flat or a circular item looking oval is not dueto a “far-near ratio” but due to a “vertical-horizontal ratio.” In otherwords, the present invention can provide an improved effect of “capableof reducing the distortion and sway of an image” not only by “decreasingthe magnification difference between the distance portion and the nearportion” but also by “decreasing the magnification difference betweenthe vertical direction and the horizontal direction to bring themagnification ratio closer to 1.” These tendencies are prominent mainlyin a portion lower than the near portion (at an eyeball rotating angleof around −25 degrees and lower).

EXAMPLE 2

[0213] Table 2-1 in FIG. 8 is a list regarding the surface refractivepowers of Example 2 according to the present invention. The diopters ofExample 2correspond to S being +6.00 and ADD being 3.00, with threekinds of prior art examples having the same diopters being listedtogether for comparison. It should be noted that Prior art example A,Prior art example B, and Prior art example C correspond to a “convexsurface progressive-power lens” in which the object side surface is aprogressive surface, a “bi-surface progressive-power lens” in which boththe object side surface and eyeball side surface are progressivesurfaces, and a “concave surface progressive-power lens in which theeyeball side surface is a progressive surface, respectively. Meanings ofterms such as DVf1 to DHn2 used in Table 2-1 are the same as those inthe above-described Table 1-1. Graphs 2-1 and 2-2 are graphs showing thesurface refractive power distributions along the main gazing lines ofExample 2 according to the present invention, with the horizontal axisindicating the lens upper side on the right hand side and the lens lowerside on the left hand side, and the vertical axis indicating the surfacerefractive power. Here, Graph 2-1 corresponds to the object sidesurface, and Graph 2-2 corresponds to the eyeball side surface. Besides,the graph shown by a solid line represents the surface refractive powerdistribution in the vertical direction along the main gazing line, andthe graph shown by a dotted line represents the surface refractive powerdistribution in the horizontal direction along the main gazing line. Itshould be noted that these are graphs for explaining the basicdifference in surface configuration, omitting a case of asphericalprocessing for eliminating astigmatism in a peripheral portion and acase of addition of a cylindrical component for coping with acylindrical diopter.

[0214] Further, Graphs A-1 and A-2, Graphs B-1 and B-2, and Graphs C-1and C-2 which are used in the above-described Example 1 are used againas graphs showing the surface refractive power distributions along themain gazing lines of the three kinds of prior art examples having thesame diopters, which are listed in Table 2-1 for comparison. Therefore,meaning of terms in these graphs are the same as those in theabove-described Example 1. The surface refractive powers at F1, N1, F2,and N2 should correspond to those in Table 2-1, and any of the averagesurface refractive powers on the object side surfaces shown byone-dotted chain lines in the horizontal direction at the middle shouldhave a deep curve of 10.50 diopter on the ground of correspondence toTable 2-1.

[0215] The next eight kinds of graphs starting with Graph 2-3-shown inFIG. 23 to FIG. 30 are graphs showing results, obtained by performingthe above-described accurate magnification calculations, ofmagnification distributions when the lens of Example 2 according to thepresent invention is viewed along the main gazing line. Meanings ofterms and symbols appended to “Graph 2-3-” are the same as those in theabove-described Example 1 other than that thick lines in the drawingsare for Example 2. Although any of the refractive indexes, objectivepowers, and eyeball rotating angles used in Example 2 and theabove-described three kinds of prior art examples was the same as thatin the above-described Example 1, only the center thickness t was set at6.0 mm close to an actual product because Example 2 and theabove-described three kinds of prior art examples have diopters of Sbeing +6.00 and ADD being 3.00.

[0216] Table 2-2 in FIG. 8 is a list of results obtained by performingaccurate magnification calculations for a specific sight line directionof Example 2 according to the present invention and three kinds of priorart examples prepared for comparison, and corresponds to theabove-described Graph 2-3-SMv (total magnification in the verticaldirection) and Graph 2-3-SMh (total magnification in the horizontaldirection). Here, meanings represented by symbols in Table 2-2 are thesame as those in the above-described Table 1-2.

[0217] SMvfn and SMhfn in Table 2-2, that is, the magnificationdifference in the vertical direction (SMvn−SMvf) and the magnificationdifference in the horizontal direction (SMhn−SMhf), show that the valuesof magnification differences of Example 2 according to the presentinvention are suppressed to as low as 0.2151 and 0.1199, whereas thoseof the prior art examples are 0.2275 and 0.1325 in A, 0.2277 and 0.1268in B, and 0.2280 and 0.1210 in C. In other words, the magnificationdifference between the distance portion and the near portion of Example2 according to the present invention are made further smaller than thoseof Prior art 1, which shows that Example 2 is improved more greatly thanPrior art 1 also in distortion and sway of an image. As is immediatelyapparent, as in Example 1, from comparison between Graph 2-3-SMv (totalmagnification in the vertical direction) and Graph 2-3-SMh (totalmagnification in the horizontal direction) resulting from accuratemagnification calculations, corresponding to Example 2 according to thepresent invention, magnification distributions of an image in thevertical direction and the horizontal direction are apparentlydifferent.

[0218] Further, it is easily read that this difference is prominentmainly in a portion lower than the middle portion (at an eyeballrotating angle of around −10 degrees and lower). As in Example 1, Graph2-3-SMv is obtained also in Example 2 by multiplying three elements,that is, values of Graph 2-3-Msv, Graph 2-3-Mpv, and Graph 2-3-Mγv, andsimilarly Graph 2-3-SMh is obtained by multiplying three elements, thatis, values of Graph 2-3-Msh, Graph 2-3-Mph, and Graph 2-3-Mγh. Here, incomparison between the elements in the vertical direction and thehorizontal direction, there is no apparent difference found between Msvand Msv, which are shape factors, whereas there is a difference foundbetween Mpv and Mph in a portion lower than the near portion (at aneyeball rotating angle of around −20 degrees and lower). Further, thereis an obvious difference between Mγv and Mγh in a portion lower than themiddle portion (at an eyeball rotating angle of around −10 degrees andlower). There is also a difference found in an upper portion of thedistance portion (at an eyeball rotating angle of around +20 degrees andupper), which is negligible because a difference existing between theexamples in a quite upper portion of the distance portion (at an eyeballrotating angle of around +30 degrees and upper) with less frequent use.

[0219] In short, it is shown, as in the above-described Example 1, thatthe major cause of the difference between Graph 2-3-SMv in FIG. 29 andGraph 2-3-SMh in FIG. 30 is the difference between Mγv and Mγh, thesecondary cause thereof is the difference between Mpv and Mph, and thereis no obvious difference found between Msv and Msh, which are almostirrelevant thereto. Further, there is no difference found among theexamples in the magnification difference between the distance and nearportions, as long as in the scale used in Example 2 of the presentinvention, in the shape factors Msv and Msh, which are regarded asreasons of improvement in Prior art 1. Note that, as in Example 1, thepresent invention can provide, also in Example 2, an improved effect of“capable of reducing the distortion and sway” not only by “decreasingthe magnification difference between the distance portion and the nearportion” but also by “decreasing the magnification difference betweenthe vertical direction and the horizontal direction to bring themagnification ratio closer to 1.” These tendencies are prominent mainlyin a portion lower than the near portion (at an eyeball rotating angleof around −25 degrees and lower).

EXAMPLE 3

[0220] Table 3-1 in FIG. 9 is a list regarding the surface refractivepowers of Example 3 according to the present invention. The diopters ofExample 3 correspond to S being −6.00 and ADD being 3.00, with threekinds of prior art examples having the same diopters being listedtogether for comparison. It should be noted that Prior art example A,Prior art example B, and Prior art example C correspond to a “convexsurface progressive-power lens” in which the object side surface is aprogressive surface, a “bi-surface progressive power lens” in which boththe object side surface and eyeball side surface are progressivesurfaces, and a “concave surface progressive-power lens in which theeyeball side surface is a progressive surface, respectively. Meanings ofterms such as DVf1 to DHn2 used in Table 3-1 are the same as those inthe above-described Table 1-1 and Table 2-1.

[0221] Graphs 3-1 and 3-2 in FIG. 11 are graphs showing the surfacerefractive power distributions along the main gazing lines of Example 3according to the present invention, with the horizontal axis indicatingthe lens upper side on the right hand side and the lens lower side onthe left hand side, and the vertical axis indicating the surfacerefractive power. Here, Graph 3-1 corresponds to the object sidesurface, and Graph 3-2 corresponds to the eyeball side surface. Besides,the graph shown by a solid line represents the surface refractive powerdistribution in the vertical direction along the main gazing line, andthe graph shown by a dotted line represents the surface refractive powerdistribution in the horizontal direction along the main gazing line. Itshould be noted that these are graphs for explaining the basicdifference in surface configuration, omitting a case of asphericalprocessing for eliminating astigmatism in a peripheral portion and acase of addition of a cylindrical component for coping with acylindrical diopter.

[0222] Further, Graphs A-1 and A-2, Graphs B-1 and B-2, and Graphs C-1and C-2 which are used in the above-described Examples 1 and 2 are usedagain as graphs showing the surface refractive power distributions alongthe main gazing lines of the three kinds of prior art examples havingthe same diopters, which are listed in Table 3-1 in FIG. 9 forcomparison. Therefore, meaning of terms in these graphs are the same asthose in the above-described Examples 1 and 2. The surface refractivepowers at F1, N1, F2, and N2 should correspond to those in theaforementioned Table 3-1, and any of the average surface refractivepowers on the object side surface shown by one-dotted chain lines in thehorizontal direction at the middle should have a shallow curve with 2.50diopter for the ground of correspondence to Table 3-1.

[0223] The next eight kinds of graphs starting with Graph 3-3-shown inFIG. 31 to FIG. 38 are graphs showing results, obtained by performingthe above-described accurate magnification calculations, ofmagnification distributions when the lens of Example 3 according to thepresent invention is viewed along the main gazing line. Meanings ofterms and symbols appended to “Graph 3-3-” are the same as those in theabove-described Examples 1 and 2 other than that thick lines in thedrawings are for Example 3. Although any of the refractive indexes,objective powers, and eyeball rotating angles used in Example 3 and theabove-described three kinds of prior art examples was the same as thatin the above-described Examples 1 and 2, only the center thickness t wasset to 1.0 mm close to an actual product because Example 3 and theabove-described three kinds of prior art examples had diopters of Sbeing −6.00 and ADD being 3.00.

[0224] Table 3-2 in FIG. 9 is a list of results obtained by performingaccurate magnification calculations for a specific sight line directionof Example 3 according to the present invention and three kinds of priorart examples prepared for comparison, and corresponds to theabove-described Graph 3-3-SMv (total magnification in the verticaldirection) and Graph 3-3-SMh (total magnification in the horizontaldirection). Here, meanings represented by symbols in Table 3-2 are thesame as those the meanings in the above-described Table 1-2 and Table2-2.

[0225] SMvfn and SMhfn in Table 3-2, that is, the magnificationdifference in the vertical direction (SMvn−SMvf) and the magnificationdifference in the horizontal direction (SMhn−SMhf), show that the valuesof magnification differences of Example 2 according to the presentinvention are at 0.0512 and 0.0726, whereas those of the prior artexamples are 0.0475 and 0.0774 in A, 0.0418 and 0.0750 in B, and 0.0363and 0.0727 in C, showing that in Example 3 the magnification differencein the vertical direction increases, whereas the magnificationdifference in the horizontal direction decreases. However, consideringthe magnification difference in the vertical direction having a lowvalue, which is ⅓ to ⅕ that of the above-described Examples 1 andExample 2, with a slight decrease in the magnification difference in thehorizontal direction, it can be said that there is not so greatmagnification difference between the distance portion and the nearportion of Example 3 according to the present invention as compared tothose of Prior art 1. Meanwhile, a study of Graph 3-3-SMv (totalmagnification in the vertical direction) and Graph 3-3-SMh (totalmagnification in the horizontal direction) obtained by performingaccurate magnification calculations corresponding to Example 3 accordingto the present invention, shows that Example 3 according to the presentinvention, as compared to the prior art examples, has the least“tendency of the magnification in the vertical direction to be smallerthan 1” especially in a portion lower than the near portion (at aneyeball rotating angle of around −20 degrees and lower), which resultsin the least “magnification difference between the vertical directionand the horizontal direction” so that distortion and sway of an imageare improved further than in the prior art examples.

[0226] It should be noted that in Graph 3-3-SMv (total magnification inthe vertical direction) in FIG. 37, there occurs a significantdifference in magnification distribution of an image between thevertical direction and the horizontal direction mainly in a portionlower than the middle portion (at an eyeball rotating angle of around−10 degrees and lower) and in an upper portion of the distance portion(at an eyeball rotating angle of around +10 degrees and upper), whereasthere occurs a difference among the examples in a portion lower than thenear portion (at an eyeball rotating angle of around −20 degrees andlower) and in a slightly upper portion of the distance portion (at aneyeball rotating angle of around +25 degrees and upper). Of them, thedifference in the slightly upper portion of the distance portion isnegligible because it is infrequently used, while that in the portionlower than the near portion is nonnegligible because it is frequentlyused. As a result, in Example 3 according to the present invention, ascompared to the prior art examples, the magnification in the verticaldirection is closest to 1 especially in the portion lower than the nearportion (at an eyeball rotating angle of around −20 degrees and lower),which results in the least “magnification difference between thevertical direction and the horizontal direction” so that distortion andsway of an image are improved further than in the prior art examples.Note that these tendencies are prominent mainly in the portion lowerthan the near portion (at an eyeball rotating angle of around −25degrees and lower). Further, there is no difference, as in Example 1 andExample 2 of the present invention, found among the examples in themagnification difference between the distance and near portions even inthe scale used in Example 3, in the shape factors Msv and Msh which areregarded as reasons of improvement in Prior art 1.

EXAMPLES 4 to 7

[0227] As examples of the present invention, there are various possiblecombinations of distributions of surface refractive powers within thescope described in claims other than the above-described Examples 1 to3. Examples 4 to 6 are shown here as applications having the samediopters as Example 1, and Example 7 as an application having the samediopters as Example 2. Lists and graphs of the surface refractive powersand results obtained by performing accurate magnification calculationsfor a specific sight line direction of these examples are shown in Table1-1 and Table 1-2 in FIG. 7 and Graphs 4-1 and 4-2 to Graphs 7-1 and 7-2in FIG. 12 to FIG. 14.

Modifications

[0228] Further, in the present invention, it is also possible to meetthe demand for custom-made product (individual design) by incorporating,into the lens design as input information, not only usual prescriptionvalues but also, for example, the distance from the corneal vertex tothe lens rear vertex, the distance from the eyeball rotating center tothe lens rear vertex, the degree of aniseiconia between right and lefteyes, the difference in height between right and left eyes, the objectdistance in near vision most frequently used, the forward tilt angle (inan up-down direction) and horizontal tilt angle (in a right-leftdirection) of a frame, the bevel position in the edge thickness of thelens, and so on, as individual factors of spectacle wearers which havebeen rarely grasped by lens manufactures. Although the present inventionhas a bi-aspherical surface configuration, it is not always necessary toprocess both surfaces after acceptance of an order to obtain the effectof the present invention. It is also advantageous in terms of cost andprocessing speed, for example, to prepare in advance “semifinishedproducts” of the object side surface meeting the object of the presentinvention, select, after acceptance of an order, from among them a“semifinished product” of the object side surface meeting the purposesuch as a prescription diopter or the above-described custom-madeproduct (individual design), and process and finish only the eyeballside surface after acceptance of the order.

[0229] As a specific example of this method, for example, previouspreparation of a bilaterally symmetrical “semifinished product” of theobject side surface is conceivable. Then, an inner shift of the nearportion in response to the convergence action of -an eye in near visioncan be incorporated by making the eyeball side surface into abilaterally asymmetrical curved surface meeting the purpose inaccordance with individual information such as the inter-vertex distanceor the object distance in the near vision. As a matter of course, thereare various conceivable means for obtaining or defining the individualinformation not only by actual measurement but also by estimation or bysetting to average or standard values, but the present invention willnot be limited to those means. Besides, it is possible to add a“correction action” for eliminating or reducing occurrence ofastigmatism and change in diopter primarily caused by impossibility ofthe sight line intersecting at right angles with the lens surface, tothe object side surface or the eyeball side surface or both curvedsurfaces of the object side surface and the eyeball side surface, inperformance of optical calculations for incorporating not only usualprescription values but also the above-described individual factors intothe lens design.

[0230] Further, it is generally known that three-dimensional rotatingmotions of eyes when we look around are based on a rule called“Listing's law.” When a prescription diopter includes a cylindricaldiopter, cylindrical axes of a spectacle lens and the eye may not matchto each other in peripheral vision even if the cylindrical axis of thelens is matched to the “cylindrical axis of the eye in front vision.” Itis also possible to add a “correction action” for eliminating orreducing occurrence of astigmatism and change in diopter caused by sucha mismatch between the cylindrical axes of the lens and the eye inperipheral vision, to a curved surface being the surface on the sidehaving a cylindrical correction action of a lens according to thepresent invention.

[0231] It should be noted that, as the definition of the “predeterminedaddition diopter” in the present invention, any of the followingdefinitions in various cases can be employed, including a case in whichthe diopter is defined as the difference between refractive powersmeasured by placing an opening of a lens meter at the far vision dioptermeasurement position F1 and at the near vision diopter measurementposition N1 on the object side surface as shown in FIG. 6; and inaddition, a case in which the diopter is defined as the differencebetween refractive powers measured by placing an opening of a lens meterat the far vision diopter measurement position F2 and at the near visiondiopter measurement position N2 on the eyeball side surface; further acase in which the diopter is defined as the difference between arefractive power measured by placing an opening of a lens meter at thefar vision diopter measurement position F2 on the eyeball side surfaceand a refractive power measured at N3 by rotating the opening of thelens meter about the eyeball rotating center position and directing ittoward the near vision diopter measurement position N2; and a case usingonly refractive power component in the horizontal direction for eachrefractive power.

Industrial Availability

[0232] As has been described, according to the present invention, abi-aspherical type progressive-power lens can be obtained which canprovide an excellent visual acuity correction for prescription valuesand a wide effective visual field with less distortion in wearing, byreducing a magnification difference of an image between a distanceportion and a near portion through correct calculation of themagnification of the image, with an influence by an “angle between asight line and a lens surface” and an “object distance” taken intoconsideration, and which makes it possible to use a “bilaterallysymmetrical semifinished product” as an object side surface and processafter acceptance of an order only an eyeball side surface into abilaterally asymmetrical curved surface coping with a convergence actionof an eye in near vision, and to reduce processing time and cost.

1. A bi-aspherical type progressive-power lens with a progressiverefractive power action dividedly allotted to a first refractive surfacebeing an object side surface and a second refractive surface being aneyeball side surface, wherein when on said first refractive surface, asurface refractive power in a horizontal direction and a surfacerefractive power in a vertical direction, at a far vision dioptermeasurement position F1, are DHf and DVf respectively, and on said firstrefractive surface, a surface refractive power in a horizontal directionand a surface refractive power in a vertical direction, at a near visiondiopter measurement position N1, are DHn and DVn respectively,relational equations, DHf+DHn<Dvf+DVn, and DHn<DVn are satisfied, andsurface astigmatism components at F1 and N1 of said first refractivesurface are cancelled by said second refractive surface so that saidfirst and second refractive surfaces together provide a far visiondiopter (Df) and an addition diopter (ADD) based on prescription values.2. The bi-aspherical type progressive-power lens according to claim 1,wherein relational equations DVn−DVf>ADD/2, and DHn−DHf<ADD/2 aresatisfied.
 3. The bi-aspherical type progressive-power lens according toclaim 1, wherein said first refractive surface is bilaterallysymmetrical with respect to one meridian passing through the far visiondiopter measurement position F1, said second refractive surface isbilaterally symmetrical with respect to one meridian passing through afar vision diopter measurement position F2 of said second refractivesurface, and a position of a near vision diopter measurement position N2on said second refractive surface is shifted inward to a nose by apredetermined distance to respond to a convergence action of an eye innear vision.
 4. The bi-aspherical type progressive-power lens accordingto claim 1, wherein said first refractive surface is a rotation surfacewith as a generatrix one meridian passing through the far vision dioptermeasurement position F1, said second refractive surface is bilaterallysymmetrical with respect to one meridian passing through a far visiondiopter measurement position F2 on said second refractive surface, and aposition of a near vision diopter measurement position N2 on said secondrefractive surface is shifted inward to a nose by a predetermineddistance to respond to a convergence action of an eye in near vision. 5.The bi-aspherical type progressive-power lens according to claim 1,wherein in a configuration of said first and second refractive surfacestogether providing the far vision diopter (Df) and the addition diopter(ADD) based on the prescription values, occurrence of astigmatism andchange in diopter caused by impossibility of a sight line intersectingat right angles with a lens surface in a wearing state are reduced. 6.The bi-aspherical type progressive-power lens according to claim 2,wherein said first refractive surface is bilaterally symmetrical withrespect to one meridian passing through the far vision dioptermeasurement position F1, said second refractive surface is bilaterallysymmetrical with respect to one meridian passing through a far visiondiopter measurement position F2 of said second refractive surface, and aposition of a near vision diopter measurement position N2 on said secondrefractive surface is shifted inward to a nose by a predetermineddistance to respond to a convergence action of an eye in near vision. 7.The bi-aspherical type progressive-power lens according to claim 2,wherein said first refractive surface is a rotation surface with as ageneratrix one meridian passing through the far vision dioptermeasurement position F1, said second refractive surface is bilaterallysymmetrical with respect to one meridian passing through a far visiondiopter measurement position F2 on said second refractive surface, and aposition of a near vision diopter measurement position N2 on said secondrefractive surface is shifted inward to a nose by a predetermineddistance to respond to a convergence action of an eye in near vision. 8.The bi-aspherical type progressive-power lens according to claim 3,wherein said first refractive surface is a rotation surface with as ageneratrix one meridian passing through the far vision dioptermeasurement position F1, said second refractive surface is bilaterallysymmetrical with respect to one meridian passing through a far visiondiopter measurement position F2 on said second refractive surface, and aposition of a near vision diopter measurement position N2 on said secondrefractive surface is shifted inward to a nose by a predetermineddistance to respond to a convergence action of an eye in near vision. 9.The bi-aspherical type progressive-power lens according to claim 2,wherein in a configuration of said first and second refractive surfacestogether providing the far vision diopter (Df) and the addition diopter(ADD) based on the prescription values, occurrence of astigmatism andchange in diopter caused by impossibility of a sight line intersectingat right angles with a lens surface in a wearing state are reduced. 10.The bi-aspherical type progressive-power lens according to claim 3,wherein in a configuration of said first and second refractive surfacestogether providing the far vision diopter (Df) and the addition diopter(ADD) based on the prescription values, occurrence of astigmatism andchange in diopter caused by impossibility of a sight line intersectingat right angles with a lens surface in a wearing state are reduced. 11.The bi-aspherical type progressive-power lens according to claim 4,wherein in a configuration of said first and second refractive surfacestogether providing the far vision diopter (Df) and the addition diopter(ADD) based on the prescription values, occurrence of astigmatism andchange in diopter caused by impossibility of a sight line intersectingat right angles with a lens surface in a wearing state are reduced.